Question: Simplify the following expression: $ t = \dfrac{9z}{-7z - 5} + \dfrac{9}{8} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{9z}{-7z - 5} \times \dfrac{8}{8} = \dfrac{72z}{-56z - 40} $ Multiply the second expression by $\dfrac{-7z - 5}{-7z - 5}$ $ \dfrac{9}{8} \times \dfrac{-7z - 5}{-7z - 5} = \dfrac{-63z - 45}{-56z - 40} $ Therefore $ t = \dfrac{72z}{-56z - 40} + \dfrac{-63z - 45}{-56z - 40} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{72z - 63z - 45}{-56z - 40} $ $t = \dfrac{9z - 45}{-56z - 40}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-9z + 45}{56z + 40}$